This really tickles my fancy. My thoughts:
1. Initiating action. These actions can be performed by selecting a cell, or range of cells, then clicking an indicator on the cell (in Google Sheets it's a small standout square along the border in the bottom right corner of the bottom-most selected cell) to initiate the action. The user can either a) click the indicator and drag down through the column to generate the values to each cell or b) double-click the indicator to fill down to the "bottom" that matches the adjacent column. Double-clicking when there are no adjacent values results in no action.
2. Sequence recognition. There are an endless number of patterns that we could recognize so we will need to identify what patterns we want to recognize. Our recognition algorithm can provide inputs to a SEQUENCE() function. Some examples of what is supported by Google's spreadsheets: https://www.benlcollins.com/spreadsheets/sequence-function
3. Support for copying a range is done by copying the selected range of cell values over and over until they fill the users target selection.
4. Multi-column selection. Other spreadsheet software support multi-column operation of these mechanisms. This is effectively just invoking the same sequence recognition pattern on each column within the selection but all within one selection.